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Incommensurate structure of AlPO4-5 and its stability

Authors:

Komatsu, Kazuki; Ikeda, Takuji; Kodaira, Tetsuya

Journal:

Acta Crystallographica Section B 82 344-351 (2026)

DOI:

https://doi.org/10.1107/S205252062600449X

B-IncStrDB ID: JorIihFWgvi Entry date: 2026-05-19 Last revision: 2026-06-26

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Chemical data

Structural Formula Sum: Al1 O4 P1 [ Help ]

Formula weight: 122 Da [ Help ]

Crystallographic data and experimental details

Crystal system: hexagonal [ Help ]

Superspace group name: P6(00γ)h [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4
2 -x2,x1-x2,x3,x4+1/3
3 -x1+x2,-x1,x3,x4+2/3
4 -x1,-x2,x3,x4+1/2
5 x2,-x1+x2,x3,x4+5/6
6 x1-x2,x1,x3,x4+1/6

a: 13.76570(17) Å [ Help ]

b: 13.76570(17) Å [ Help ]

c: 8.37040(12) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 1373.64(3) Å3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.000000 0.000000 0.367100

Z: 12 [ Help ]

Cell determination reflection Nb.: 17280 [ Help ]

θ(min) for cell determination: 2.94 ° [ Help ]

θ(max) for cell determination: 26.33 ° [ Help ]

Cell measurement temperature: 295 K [ Help ]

μ: 0.672 mm-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.44.103a (Rigaku Oxford Diffraction, 2025) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.81 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 8733 [ Help ]

Nb. of observed reflections: 8597 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0824 [ Help ]

wR(obs): 0.2203 [ Help ]

R(all): 0.0835 [ Help ]

wR(all): 0.2207 [ Help ]

S(all): 7.4888 [ Help ]

S(obs): 7.5361 [ Help ]

Nb. of reflections: 8733 [ Help ]

Nb. of parameters: 252 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: calc w=1/[σ2(Fo2)+(0.02P)2+0.0000P] where P=(Fo2+2Fc2)/3 [ Help ]

Δ/σ(max): 0.0199 [ Help ]

Δ/σ(mean): 0.0023 [ Help ]

Δρ(max): 0.66 e_Å-3 [ Help ]

Δρ(min): -0.67 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Absolute structure remarks: 0 of Friedel pairs used in the refinement [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol x y z ADP type Uiso/equiv Symmetry multiplicity Occupancy Coords from (d)iffraction or (c)alculated
P1 P 0.45425(7) 0.33235(7) 0.92319(11) Uani 0.0221(4) 6 1 d
P2 P 0.33328(7) 0.45551(7) 0.42294(11) Uani 0.0217(4) 6 1 d
Al1 Al 0.33220(7) 0.45424(7) 0.79830(11) Uani 0.0123(4) 6 1 d
Al2 Al 0.45537(7) 0.33311(7) 0.29851(11) Uani 0.0119(4) 6 1 d
O1 O 0.42184(18) 0.2104(2) 0.8603(4) Uani 0.0353(11) 6 1 d
O7 O 0.2102(2) 0.42125(17) 0.3610(4) Uani 0.0336(11) 6 1 d
O4 O 0.3630(2) 0.3636(2) 0.8602(4) Uani 0.0375(11) 6 1 d
O6 O 0.4230(3) 0.5794(3) 0.3619(4) Uani 0.0390(12) 6 1 d
O3 O 0.5779(3) 0.4238(3) 0.8613(4) Uani 0.0405(12) 6 1 d
O8 O 0.3688(2) 0.3682(2) 0.3618(4) Uani 0.0397(12) 6 1 d
O5 O 0.3333(2) 0.4553(2) 0.6121(4) Uani 0.0471(14) 6 1 d
O2 O 0.4551(2) 0.3335(2) 1.1129(4) Uani 0.0477(14) 6 1 d

ADP components: [ Help ]

Atom site label Atom site symbol U11 U22 U33 U12 U13 U23
P1 P 0.0222(5) 0.0184(4) 0.0268(6) 0.0109(4) 0.0019(3) 0.0015(3)
P2 P 0.0194(5) 0.0225(5) 0.0265(6) 0.0130(4) 0.0010(3) 0.0011(3)
Al1 Al 0.0100(4) 0.0141(4) 0.0136(5) 0.0067(4) -0.0021(3) -0.0021(3)
Al2 Al 0.0139(5) 0.0116(4) 0.0131(5) 0.0087(4) -0.0007(3) -0.0008(3)
O1 O 0.0296(13) 0.0223(13) 0.0556(15) 0.0143(12) -0.0002(13) -0.0017(11)
O7 O 0.0241(13) 0.0259(12) 0.0505(15) 0.0122(12) -0.0013(12) 0.0001(13)
O4 O 0.0362(15) 0.0363(15) 0.0463(13) 0.0229(12) -0.0022(13) 0.0001(13)
O6 O 0.0387(16) 0.0364(16) 0.0485(14) 0.0238(12) 0.0061(12) 0.0047(12)
O3 O 0.0362(15) 0.0377(16) 0.0517(15) 0.0216(12) 0.0063(12) 0.0068(12)
O8 O 0.0355(15) 0.0351(15) 0.0519(15) 0.0202(12) 0.0028(13) -0.0055(13)
O5 O 0.0500(18) 0.0547(18) 0.0385(17) 0.0275(15) -0.0041(13) 0.0012(13)
O2 O 0.0511(18) 0.0500(18) 0.0417(18) 0.0250(15) -0.0008(14) 0.0040(13)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): [ Help ]

Wave vector code q_1
1 1
2 2

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
1 P1 x 1
2 P1 y 1
3 P1 z 1
4 P1 x 2
5 P1 y 2
6 P1 z 2
7 P2 x 1
8 P2 y 1
9 P2 z 1
10 P2 x 2
11 P2 y 2
12 P2 z 2
13 Al1 x 1
14 Al1 y 1
15 Al1 z 1
16 Al1 x 2
17 Al1 y 2
18 Al1 z 2
19 Al2 x 1
20 Al2 y 1
21 Al2 z 1
22 Al2 x 2
23 Al2 y 2
24 Al2 z 2
25 O1 x 1
26 O1 y 1
27 O1 z 1
28 O1 x 2
29 O1 y 2
30 O1 z 2
31 O7 x 1
32 O7 y 1
33 O7 z 1
34 O7 x 2
35 O7 y 2
36 O7 z 2
37 O4 x 1
38 O4 y 1
39 O4 z 1
40 O4 x 2
41 O4 y 2
42 O4 z 2
43 O6 x 1
44 O6 y 1
45 O6 z 1
46 O6 x 2
47 O6 y 2
48 O6 z 2
49 O3 x 1
50 O3 y 1
51 O3 z 1
52 O3 x 2
53 O3 y 2
54 O3 z 2
55 O8 x 1
56 O8 y 1
57 O8 z 1
58 O8 x 2
59 O8 y 2
60 O8 z 2
61 O5 x 1
62 O5 y 1
63 O5 z 1
64 O5 x 2
65 O5 y 2
66 O5 z 2
67 O2 x 1
68 O2 y 1
69 O2 z 1
70 O2 x 2
71 O2 y 2
72 O2 z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
1 0 0.02345(11)
2 -0.00514(8) 0.01465(10)
3 0.02805(18) -0.0186(2)
4 0.00101(10) -0.00047(10)
5 0.00063(9) -0.00105(9)
6 -0.00274(15) 0.00108(15)
7 -0.00073(11) 0.01479(10)
8 -0.00063(11) 0.01429(10)
9 0.03211(15) 0.0075(2)
10 0.00195(9) 0.00006(9)
11 0.00153(9) -0.00083(9)
12 0.00194(14) -0.00052(15)
13 -0.00319(11) 0.01541(10)
14 -0.01207(12) 0.02034(11)
15 0.0149(2) 0.03042(16)
16 -0.00063(9) 0.00089(9)
17 0.00006(11) 0.00100(10)
18 0.00028(16) 0.00267(14)
19 -0.00672(10) 0.01273(10)
20 -0.00693(11) 0.01331(10)
21 0.03161(15) 0.0100(2)
22 0.00002(9) 0.00175(10)
23 0.00103(9) 0.00173(9)
24 -0.00057(15) -0.00218(14)
25 0.0039(3) 0.0157(3)
26 -0.0118(3) 0.0117(3)
27 0.0622(4) -0.0171(6)
28 0.0014(3) -0.0008(3)
29 0.0011(3) 0.0004(2)
30 -0.0020(6) -0.0030(4)
31 0.0029(3) 0.0089(3)
32 -0.0056(3) 0.0058(3)
33 0.0220(5) 0.0206(5)
34 0.0009(2) -0.0017(2)
35 0.0001(3) -0.0035(2)
36 0.0043(3) -0.0001(5)
37 0.0039(3) 0.0149(3)
38 -0.0102(3) 0.0106(3)
39 -0.0008(4) -0.0016(5)
40 0.0004(2) -0.0011(2)
41 -0.0010(2) 0.0013(2)
42 -0.0035(4) 0.0056(3)
43 0.0031(4) 0.0078(3)
44 -0.0055(3) 0.0060(3)
45 0.0102(5) -0.0330(4)
46 0.0019(3) -0.0036(2)
47 0.0023(3) -0.0031(2)
48 0.0026(4) -0.0051(4)
49 0.0035(3) 0.0158(3)
50 -0.0109(3) 0.0116(3)
51 0.0160(6) -0.0521(4)
52 0.0017(3) -0.0016(3)
53 0.0007(3) -0.0022(3)
54 -0.0006(5) 0.0008(4)
55 0.0015(3) 0.0086(3)
56 -0.0071(3) 0.0069(3)
57 0.0726(4) 0.0197(7)
58 0.0018(3) 0.0015(3)
59 0.0026(3) 0.0007(3)
60 -0.0025(6) 0.0021(5)
61 -0.0225(4) 0.0291(3)
62 -0.0022(4) 0.0476(3)
63 0.0266(5) 0.0209(5)
64 0.0001(4) 0.0044(3)
65 -0.0018(4) 0.0010(4)
66 0.0034(5) 0.0009(5)
67 -0.0222(4) 0.0417(3)
68 0.0047(4) 0.0361(3)
69 0.0335(5) -0.0050(5)
70 -0.0003(3) -0.0017(4)
71 0.0041(3) -0.0015(4)
72 -0.0028(5) -0.0039(5)